Greek Geometry - Euclid, Pythagoras, Archimedes and Thales Greek Geometry Greek Geometry - Euclid, Pythagoras, Archimedes and Thales . This article is a part of the guide: Select from one of the other courses available: Discover 44 more articles on this topic Don't miss these related articles: 8.6Mental Hospitals Save this course for later Don't have time for it all now? No problem, save it as a course and come back to it later. Like Explorable? Take it with you wherever you go. Download Explorable Now! Subscribe to our RSS Feed Like us on Facebook Share this page on your website: <a href="">Greek Geometry</a> Geometry can conceivably lay claim to being the oldest branch of mathematics outside arithmetic, and humanity has probably used geometrical techniques since before the dawn of recorded history. Initially, as with the Egyptians, geometry originated from practical necessity and the need to measure land; the word 'Geometry' means 'Earth Measuring'. This article is a part of the guide: Select from one of the other courses available: Discover 44 more articles on this topic Don't miss these related articles: .

Euclid, illustrating geometry in "The School of Athens", by Raffaello Sanzio (Public Domain) Certainly, for measuring boundaries and for erecting buildings, humans need to have some inbuilt mechanism and instinct for judging distances, angles, and height. As civilizations developed, these instincts were augmented by observations and procedures gained from experience, experimentation, and intuition. The Babylonians were certainly skilled geometers, and the Egyptians developed a rich and complex mathematics based around surveying. Both of these cultures would pass their information on to the Greeks. . The Start of Greek Geometry The Egyptians and the Babylonians were not really interested in finding out axioms and underlying principles governing geometry. Their approach was very pragmatic and aimed very much at practical uses. The Babylonians, for example, assumed that Pi was exactly 3, and saw no reason to change this. The Egyptian mathematicians had no structure to their geometry, just a collection of rules and solutions aimed at specific circumstances, such as calculating the volume of a truncated pyramid. They also used trigonometry at that point, in development of a subset of geometry, for surveying and for measuring the dimensions of pyramids. These cultures did not appear to use deductive reasoning to uncover geometric techniques from first principles.

Instead, they used trial and error and, if a solution was not readily available, used trial and error to arrive at an approximation. However, these cultures laid the foundations of Greek geometry and influenced the Greeks, who would bring a deductive methodology to geometry, trying to find elegant rules underpinning the field. . Early Greek Geometry Thales of Miletus (Public Domain) The early history of Greek geometry is unclear, because no original sources of information remain and all of our knowledge is from secondary sources written many years after the early period. However, we can still see a decent overview and also start to look at some of the great names, the Greek mathematicians who would shape the course of Greek geometry. The first, and one of the greatest names, is Thales of Miletus, a mathematician living in the 6th century BCE. He is regarded as the father of geometry and began the process of using deduction from first principles. It is believed that he travelled to Egypt and Babylon, picking up geometric techniques from these cultures, and he certainly would have had access to their work. Thales strongly believed that reasoning should supersede experimentation and intuition, and began to look for solid principles upon which he could build theorems.

This introduced the idea of proof into geometry and he proposed some axioms that he believed to be mathematical truths. A circle is bisected by any of its diameters The base angles of an isosceles triangle are equal When two straight lines cross, the opposing angles are equal An angle drawn in a semi-circle is a right angle Two triangles with one equal side and two equal angles are congruent Thales is credited with devising a method for finding the height of a ship at sea, a technique that he used to measure the height of a pyramid, much to the delight of the Egyptians. For this, he had to understand proportion and possibly the rules governing similar triangles, one of the staples of trigonometry and geometry. It is unclear exactly how Thales decided that the above axioms were irrefutable proofs, but they were incorporated into the body of Greek mathematics and the influence of Thales would influence countless generations of mathematicians. Pythagoras Pythagoras (Public Domain) Probably the most famous name during the development of Greek geometry is Pythagoras , even if only for the famous law concerning right angled triangles. This mathematician lived in a secret society which took on a semi-religious mission.

From this, the Pythagoreans developed a number of ideas and began to develop trigonometry. The Pythagoreans added a few new axioms to the store of geometrical knowledge. The sum of the internal angles of a triangle equals two right angles *(180o). The sum of the external angles of a triangle equals four right angles (360o). The sum of the interior angles of any polygon equals 2n-4 right angles, where n is the number of sides. The sum of the exterior angles of a polygon equals four right angles, however many sides. The three polygons, the triangle, hexagon, and square completely fill the space around a point on a plane - six triangles, four squares and three hexagons. In other words, you can tile an area with these three shapes, without leaving gaps or having overlaps. For a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Most of these rules are instantly familiar to most students, as basic principles of geometry and trigonometry. One of his pupils, Hippocrates , took the development of geometry further.

He was the first to start using geometrical techniques in other areas of maths, such as solving quadratic equations, and he even began to study the process of integration. He studied the problem of Squaring the Circle (which we now know to be impossible, simply because Pi is an irrational number). He solved the problem of Squaring a Lune and showed that the ratio of the areas of two circles equalled the ratio between the squares of the radii of the circles. Euclid Euclid meant that all mathematical statements should be proved ( Euclid's Elements ) Alongside Pythagoras, Euclid is a very famous name in the history of Greek geometry. He gathered the work of all of the earlier mathematicians and created his landmark work, 'The Elements,' surely one of the most published books of all time. In this work, Euclid set out the approach for geometry and pure mathematics generally, proposing that all mathematical statements should be proved through reasoning and that no empirical measurements were needed. This idea of proof still dominates pure mathematics in the modern world. Archimedes Archimedes was a great mathematician and was a master at visualising and manipulating space.

He perfected the methods of integration and devised formulae to calculate the areas of many shapes and the volumes of many solids. He often used the method of exhaustion to uncover formulae. For example, he found a way to mathematically calculate the area underneath a parabolic curve; calculated a value for Pi more accurately than any previous mathematician; and proved that the area of a circle is equal to Pi multiplied by the square of its radius. He also showed that the volume of a sphere is two thirds the volume of a cylinder with the same height and radius. This last discovery was engraved into his tombstone. Apollonius of Perga (262 - 190 BCE) Appolonius of Pergia (Public Domain) Apollonius was a mathematician and astronomer, and he wrote a treatise called 'Conic Sections.' Apollonius is credited with inventing the words ellipse, parabola, and hyperbola, and is often referred to as the Great Geometer. He also wrote extensively on the ideas of tangents to curves, and his work on conics and parabolas would influence the later Islamic scholars and their work on optics. .

Greek Geometry and Its Influence Greek geometry eventually passed into the hands of the great Islamic scholars, who translated it and added to it. In this study of Greek geometry, there were many more Greek mathematicians and geometers who contributed to the history of geometry, but these names are the true giants, the ones that developed geometry as we know it today. . Who Is Euclid and What Did He Do? Anyone interested in Greek history, ancient cultures, mathematics, physics, and natural sciences might be interested to learn about Euclid and his accomplishments. He is mentioned in nearly every mathematical textbook, and he is referenced in lots of historical texts and scientific texts as well. He is credited with developing many ideas, but first and foremost, he is understood to have been one of the greatest thinkers of all time. Euclid and His Accomplishments Euclid ’s story, although well known, is also something of a mystery. He lived lots of his life in Alexandria , Egypt, and developed many mathematical theories. He is most famous for his works in geometry, inventing many of the ways we conceive of space, time, and shapes.

He wrote one of the most famous books that is still used today to teach mathematics, Elements, which was well received at its time and also is praised today for its thought and understanding. This wasn’t the first time that people were writing about mathematics, and many other people developed some of the theories he presented in his text. However, what is most important to remember is that he was the first person to write a complete, coherent review of all geometry theory as he understood it. Euclid As the Father of Geometry A common misconception is that Euclid invented all concepts of geometry. This is certainly not so, as he really only pulled together ideas and developed them as his own within a textbook. However, he definitely developed the discipline in this regard, making it a concrete, organized study that people could learn from by following his written work. He is also famous for his theories on other parts of life: in Optiks, he discusses perspective and gives insight to how we view the world through our eyes. With geometric principles, other mathematicians in later centuries were able to develop upon his work. In this regard, he is understood to be the Father of Geometry since he paved the way for so many future thinkers to expand upon his organized ideas.

Other thinkers have even used his geometric method as a foil, in which they have expanded thought in a completely different direction. Euclid As a Scholar of Ancient Greece Today, we understand Ancient Greek culture as classical, in which thought, discussion, mathematics, sciences, and the arts developed and flourished as never before within Greece. Euclid was a part of that culture. Euclid existed around 300 BC, and he was a prominent figure in Greek culture at the time as a thinker and scholar . He was part of a new tradition of questioning thought, understanding the changing world, and developing ideas so that we could better understand the patterns in the world around us. He, among other Ancient Greek scholars, has left a legacy of thought that many scholars and academics today continue to follow. Euclid's Life Like many of the best thinkers of our human history, many elements of Euclid’s life remain mysterious to us. He was in no way documented biographically, at least in terms of detail and depth. He was mentioned by several other Greek thinkers, such as Pappas of Alexandria . Praclus is also known to have written about him.

These quotes about him are also not certain, since much history about scholars was in fact legend and myth in the times of Ancient Greece. Historians today certainly try to reconstruct his life history and better understand his work in contexts that we are now aware of today – a man of such impact during his time is still recognized today as a hero of thought. For more information on Euclid you can read directly from his textbook Elements, which is available at amazon.com . Euclid - Father of Geometry - Mathgreats and great math Euclid - Father of Geometry Great Math Kathy Reck ﻿﻿Known as a scholar, thinker, and the Father of Geometry, Euclid of Alexandria is the Greek mathematician who wrote the book of Elements. In addition to Euclid's own theories, Elements included work from mathematicians Thales, Pythagoras, Hippocrates, Theaetuetus, and Eudoxus, spanning the time period 600 BC - 300 BC. The name Euclid was popular during his lifetime, making it important to distinguish him from the rest of the Euclids, as Euclid of Alexandria.

Euclid is known for his development of axioms (or assumptions, or common notions), which allowed mathematicians to make deductions about mathematical problems. Quote: The laws of nature are but the mathematical thoughts of God. ﻿ Videos below (Part 1 and Part 2) about the Euclid's book of Elements. Sources: "Euclid of Alexandria." Euclid of Alexandria. N.p., n.d. Web. 11 May 2014 "Euclid of Alexandria." Euclid Summary. N.p., n.d. Web. 1 May 2014. Waerden, Bartel Leendert Van Der. "Euclid (Greek Mathematician)." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 11 May 2014 Create a free website Euclid: Biography & Father Of Geometry | Online Homework Help | SchoolWorkHelper Euclid: Biography & Father Of Geometry You are here: PDF Very little is known of the father of geometry, also known as Euclid. Records show that he lived somewhere around 300 B.C., but that date is sketchy. He was a Greek mathematician and is probably best known for his work Elements.

Since little is known about the personal life of Euclid, it is difficult to do a biography on him. His chief work, entitled Elements, is a comprehensive treatise on mathematics. It includes 13 volumes that entail such subjects as plane geometry, dealing with the properties of flat surfaces and of planar figures, such as the triangle; proportion in general, a particular kind of relation between groups of numbers or quantities; the properties of numbers; incommensurable magnitudes; and solid geometry, branch of geometry that deals with the properties and measurement of geometric figures in three-dimensional space. Some people say that the geometrical sections of Elements were actually rearrangements of Exodus previous work. However Euclid himself is said to have made several discoveries in his Number Theory, which is a branch of mathematics that deals with the properties and relationships of numbers. Most historians believe Euclid was educated at Athens. His teachers may have included pupils of Plato, who was a philosopher and one of the most influential thinkers in Western philosophy. Euclid tought geometry in Alexandria and opened a school of mathematics there.

He also wrote Data, which was a collection of geometrical theorems; Phenomena, a description of the heavens; and The Division of the Scale, which is a mathematical discussion of music. But yet again many historians believe many of these works (other than the Elements) were spuriously credited to him, others disagree and say that indeed his works are that of his own. Euclid’s Elements was used as a text for 2000 years, and even today a modified version of its first few books forms the basis of high school instruction in plane geometry. The first printed edition of Euclid’s works was a translation from Arabic to Latin, which appeared at Venice in 1482. Euclid is called the father of geometry. He has earned the respect from all mathematicians, and is regarded as the creator of the Elements, which is based on almost every point of geometry.

Students learn about him every time they open their math book Related posts: Euclid of Alexandria [ Back to KISH Home Page ] Euclid of Alexandria Euclid of Alexandria was born about 325 BC and he died about 265 BC He is called the Father of Geometry, and is best known for his treatise on mathematics, The Elements. It is said that this treatise may make Euclid the leading mathematics teacher of all time. Euclid most likely came from a rich family, because as a young child, he went to Platoï¿½s school in ancient Greece, where only the rich were educated. After he finished school he went to Alexandria, where he discovered and wrote his theories on geometry. Euclid of Alexandria is often confused with Euclid of Meguro, who was also a leading mathematician. Euclid was a popular name at that time, but The Elements set Euclid of Alexandria apart from all the others.

The Elements consists of 13 Volumes that summarize, describe, and explain all of the rules of geometry that we use today: Volumes 1-6: Plane Geometry; Volumes 7-9: Number Theory; Volume 10: Exodusï¿½ Theory of Irrational Numbers; Volumes 11-13: Solid Geometry. The first edition of The Elements was printed in 1492, and millions of copies have been sold since then. It was pulled out of schools in 1901, but the theories and principles remained the same, simply rewritten in a modern form. The Elements begins with definitions and five postulates. The first three postulates are postulates of construction; foe example, the first postulate states that it is possible to draw a straight line between any two points. The postulates assume that the existence of points, lines, circles, and other geometric objects are deduced from the fact that points, lines, etc. actually exist. Euclidï¿½s postulates led to Euclidean Geometry, and it wasnï¿½t until the 19th century that they were dropped, and non-Euclidean geometry was studied.

In his treatise, Euclid also wrote axioms, which he called "common notions". They arenï¿½t specific geometrical properties, but they are assumptions that allow mathematics to proceed as a deductive science. Euclidï¿½s Elements is remarkable for the clarity with which the theorems are stated and proved. The standard of rigor was to become a goal for the inventors of calculus centuries later. Euclid wrote his treatise after such pupils of Plato as Eudoxus, and before Archimedes. He was the leader of a team of mathematicians working at Alexandria, and they all contributed to writing the "Complete Works of Euclid", even continuing to write under Euclidï¿½s name after his death. He is described as being nice, but often sarcastic. Without his work, and his ability to compile all of his ideas into a massive format, Euclid of Alexandria would never have earned the title of the Father of Geometry.

Euclid, the Father of Geometry - Greek Mathematics Euclid, the Father of Geometry Greek Mathematics Share this page on your website: <a href="">Euclid, the Father of Geometry</a> Greek Mathematics Euclid enters history as one of the greatest of all mathematicians and he is often referred to as the father of geometry. The standard geometry most of us learned in school is called Euclidian Geometry. This article is a part of the guide: Select from one of the other courses available: Discover 44 more articles on this topic Don't miss these related articles: . Statue of Euclid in Oxford (Public Domain) Euclid gathered up all of the knowledge developed in Greek mathematics at that time and created his great work, a book called 'The Elements' (c300 BCE). This treatise is unequaled in the history of science and could safely lay claim to being the most influential non-religious book of all time. Euclid probably attended Plato's academy in Athens before moving to Alexandria, in Egypt. At this time, the city had a huge library and the ready availability of papyrus made it the center for books, the major reasons why great minds such as Heron of Alexandria and Euclid based themselves there. .

Euclid's Elements Euclid's Elements Title Page (Public Domain) Euclid's great work consisted of thirteen books covering a vast body of mathematical knowledge, spanning arithmetic, geometry and number theory. The books are organized by subjects, covering every area of mathematics developed by the Greeks: Books I - IV, and Book VI: Plane Geometry Books XI - XIII: Solid Geometry Books V and X: Magnitudes and Ratios Books VII - IX: Whole Numbers The basic structure of the elements begins with Euclid establishing axioms, the starting point from which he developed 465 propositions, progressing from his first established principles to the unknown in a series of steps, a process that he called the 'Synthetic Approach.' He looked at mathematics as a whole, but was concentrated on geometry and that particular discipline formed the basis of his work. . . Euclid's Axioms Euclid based his approach upon 10 axioms, statements that could be accepted as truths. He called these axioms his 'postulates' and divided them into two groups of five, the first set common to all mathematics, the second specific to geometry.

Some of these postulates seem to be self-explanatory to us, but Euclid operated upon the principle that no axiom could be accepted without proof. Euclid's First Group of Postulates - the Common Notions: Things which are equal to the same thing are also equal to each other If equals are added to equals, the results are equal If equals are subtracted from equals, the remainders are equal Things that coincide with each other are equal to each other The whole is greater than the part From Euclids Elements Book I, Proposition 3( Creative Commons ) The remaining five postulates were related specifically to geometry: A straight line can be drawn between any two points. Any finite straight line can be extended indefinitely in a straight line. For any line segment, it is possible to draw a circle using the segment as the radius and one end point as the center. All right angles are congruent (the same). If a straight line falling across two other straight lines results in the sum of the angles on the same side less than two right angles, then the two straight lines, if extended indefinitely, meet on the same side as the side where the angle sums are less than two right angles.

Euclid felt that anybody who could read and understand words could understand his notions and postulates but, to make sure, he included 23 definitions of common words, such as 'point' and 'line', to ensure that there could be no semantic errors. From this basis, he built his entire theory of plane geometry, which has shaped mathematics, science and philosophy for centuries. He proved that it is an impossibility to find the 'largest prime number,' because taking the largest known prime number and adding one to the product of all previous primes and the largest prime will give you another, larger prime number. . Euclid's Influence The reason that Euclid was so influential is that his work is more than just an explanation of geometry or even of mathematics. The way in which he used logic and demanded proof for every theorem shaped the ideas of western philosophers right up until the present day. Great philosopher mathematicians such as Descartes and Newton presented their philosophical works using Euclid's structure and format, moving from simple first principles to complicated concepts. Abraham Lincoln was a fan, and the US Declaration of Independence used Euclid's axiomatic system.

Apart from the Elements, Euclid also wrote works about astronomy, mirrors, optics, perspective and music theory, although many of his works are lost to posterity. Certainly, he can go down in history as one of the greatest mathematicians of all time, and he was certainly one of the giants upon whose shoulders Newton stood. . Euclid Biography - Childhood, Life Achievements & Timeline Scientists Euclid Biography Euclid was a renowned Greek mathematician, known as the âFather of Geometryâ. This biography profiles his childhood, life, works, achievements and timeline. 198 Mathematician - Euclidean Geometry, Euclid's Elements and Euclidean Algorithm Nationality Greece Image Credit Euclid was a great Greek mathematician. Although little is known about his early and personal life, he went on to contribute greatly in the field of mathematics and came to known as the âFather of Geometryâ, Euclid is known to have taught mathematics in Ancient Egypt during the reign of Ptolemy I. He wrote âElementsâ, the most influential mathematical works of all time, which served as the main textbook for teaching mathematics from its publication until the late 19th or early 20th century.

Elements aroused interest of the Western World and mathematicians around the globe for over 2000 years. Euclid used the âsynthetic approachâ towards producing his theorems, definitions and axioms. Apart from being a tutor at the Alexandria library, Euclid coined and structured the different elements of mathematics, such as Porisms, geometric systems, infinite values, factorizations, and the congruence of shapes that went on to contour Euclidian Geometry. His works were heavily influenced by Pythagoras, Aristotle, Eudoxus, and Thales to name a few. Childhood & Early Life Very little information is available about Euclid but it is presumed that he was born around 330 B.C in Tyre. Going by the accounts of certain Arabic authors, he came from a rich background. His father was âNaucratesâ while his grandfather was Zenarchus. It is said that he was a Greek born in Tyre and lived in Damascus throughout his life. However, there is no certain evidence if he was the same person as Euclid of Alexandria is often confused with Euclid of Megara, another man who was a philosopher and lived at the time of Plato.

Since lack of biographical information is rather unusual for this period, many researchers believe that Euclid may have not existed at all and, in fact, his works may have been written by a team of mathematicians who took the name Euclid. But this hypothesis is again rejected by scholars, citing lack of solid evidence. It is also said that he studied in Platoâs ancient school in Athens, a place that was only meant for affluent people. He got his mathematical training from the students of Plato. Career Euclidâs âElementsâ is considered as one of the most influential works in the history of mathematics, from the time of its publication until the late 19th or early 20th century. It actually served as the main textbook for teaching mathematics during this period. In his Elements, he deduced the principles of âEuclidean geometryâ from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor. In addition to his most famous work âElementsâ, there are at least five works of Euclid that have survived to this day. They seem to follow the same logical structure as followed in Elements.

They are âDataâ, âOn Divisions of Figures', 'Catoptrics', 'Phaenomena' and 'Optics'. In addition to the abovementioned works, there are a few other works that are attributed to Euclid but have been lost. These works include âConicsâ, âPseudariaâ, âPorismsâ, âSurface Lociâ and âOn the Heavy and the Lightâ. Euclid's Elements âElementsâ is a mathematical and geometric treatise consisting of 13 books written by this great ancient Greek mathematician in Alexandria, Ptolemaic Egypt c. 300 BC. Euclidâs âElementsâ is a collection of definitions, postulates, theorems and constructions and also the mathematical proofs of the propositions. All the 13 books cover Euclidean geometry and the ancient Greek elementary number theory. It also includes geometric algebra, which helps in solving many algebraic problems, including the problem of finding the square root of a number.

The Elements is the second oldest existing Greek mathematical treatise after Autolycus' âOn the Moving Sphereâ and has proven instrumental in the development of logic and modern science. First time printed in 1482 in Venice, âElementsâ is one of the very earliest mathematical works to be printed after the invention of the printing press. It is considered as the most successful and influential textbook ever written and believed to be second only to the holy Bible in the number of editions brought out. It is said more than 1000 editions of âElementsâ were brought out since the time printing came into existence. Other Works âElementsâ was Euclidâs most famous work and continues to influence mathematics even to this day but he wrote a number of other books as well. At least 5 works of Euclid have survived to this day. Data: This book holds 94 propositions and basically deals with the nature and implications of "given" information in geometrical problems. On Divisions of Figures: Another important work of Euclid but survives only partially in Arabic translation.

It resembles a work (3rd century) of âHeron of Alexandriaâ Catoptrics: It is another important work that is related to the mathematical theory of mirrors. J J O'Connor and E F Robertson, however, consider 'Theon of Alexandria' as the real author. Phaenomena: It throws light on spherical astronomy. It is strikingly similar to âOn the Moving Sphereâ by Autolycus of Pitane, who flourished around 310 BC. Optics: This work shares knowledge about theory of perspective and is the earliest surviving Greek treatise on perspective. Apart from the five abovementioned extant works, there are some other works attributed to Euclid, but have been lost. These are âConicsâ, âPorismsâ, âPseudariaâ and âSurface Lociâ. In addition to these, various Arabic sources consider Euclid as author of several works on mechanics. Personal Life & Legacy There is not much information and records relating to Euclidâs personal life but historians believe that he breathed his last around 260 B.C.

His most famous book âThe Elementâ was eventually translated from Arabic to Latin by Campanus. The first printed addition of the same appeared in 1482 in Venice. In 1570, John Dee translated âThe Elementâ in English. Deeâs lectures were able to revive interest in mathematics in England. An Italian mathematician, Girolamo Saccheri, in 1733 tried for years to outdo the works of Euclid but his attempts to refute it went futile as he could not even find a single flaw in Euclidâs theories. Eventually, he gave up and published âEuclid Cleared of Every Flawâ. The legacy that Euclid left behind is immense. He inspired personalities such as Abraham Lincoln, who used to religiously carry âThe Elementsâ with him everywhere and used to quote the genius in his speeches. Euclid influenced great philosophers and mathematicians such as Newton and Descartes who propounded their philosophical works using Elucidâs format and structure. They also moved from simple principles towards complicated concepts just like Elucid.

Top 10 Facts You Did Not Know About Euclid The name âEuclidâ means "renowned, gloriousâ. His book âElementsâ served as the main textbook for teaching mathematics from the time of its publication to until around early 20th century. Most of the other Greek mathematicians from Archimedes onward referred to him as "the author of Elements" and not by name. Some researchers are of the belief that Euclid was not a historical character and that his works were written by a team of mathematicians who collectively took the name Euclid. However, there is little evidence to support this hypothesis. Euclidâs Optics was the first surviving Greek dissertation on the perspective of optics. His work âDivisions of Figuresâ survives only partially in Arabic translation. A detailed biography of Euclid was given by Arabian authors though researchers believe the work to be completely fictitious. Medieval translators and editors often confused Euclid with the philosopher Eukleides of Megara who lived about a century before.

The geometrical system he described in the âElementsâ is referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century. It is often said that âElementsâ is one of the most translated, published, and studied of all the books produced in the Western world. Translate this page to Spanish, French, Hindi, Portuguese Pictures of Euclid Part III. Mathematics Advancements by Muslims Part III. Mathematics Advancements by Muslims Part III. Mathematics Advancements by Muslims: Introduction: Just as with science, the Muslims learned from the Greeks, Egyptians, Indians, and Babylonians. Many translations took place in the House of Wisdom in Baghdad, the capital of the Abbasid Empire. The Muslim scholars there translated the works of the Greeks who loved mathematics and geometry, including Euclid's work on geometry. They borrowed from India a number system that had a zero and rewrote it as their own. They borrowed from the Babylonians whose number system was based on 60 (just like the minutes in an hour), and from the ancient Egyptians who had the math and geometry skills to build incredible pyramids.

So from the beginning, "Arabic math" was a mixing of international knowledge. But the Muslims made additional contributions of their own, and through their study and written work, they preserved the knowledge of mathematics that otherwise might have been lost to the world. Arithmetic: Al-Khashi (from Persia, 15th century) invented decimal fractions: 5.25 In Khwarizmi's own words what he wanted to teach: "...what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, lawsuits, and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computations, and other objects of various sorts and kinds are concerned..." The Egyptians were very advanced in geometry and could build great pyramids. The Greeks loved geometry. The most famous Greek mathematician was Euclid who wrote about geometry. The Arabs translated and improved upon his work. The Hebrews also had made important contributions to mathematics that were studied by the Arabs. The idea of trigonometry was originally from the Greeks, by Hipparchus in 140 BCE. The Muslims further developed trigonometry from their work in astronomy.

Today astronomers use trigonometry for calculating distances to stars, and for measuring distances and heights of buildings, trees, etc. A. Arabic Numerals One of the greatest advances was the introduction of "Arabic" numerals. The "Arabic" numerals were influenced by India's mathematics. It is a system based on place values and a decimal system of tens. This system had a zero to hold a place. These numbers were much easier to use for calculation than the Roman system which used numbers, like I, V, X, L, C, M, etc. Addition, subtraction, multiplication and division now became easy. Top: Western Arabic or Hindu-Arabic Numerals Below: Modern Arabic numerals which developed from them With Arabic numerals, simple fractions and decimal fractions were also possible. Fractions and decimal fractions were also described by Muslim mathematicians during the Middle Ages. B. The Development of Algebra. Al Khwarizmi wrote the first book on algebra. (The name "algebra" was first used by him.) Al Khwarizmi was born about 790 in Baghdad (now in Iraq) and died about 850.

The word for "Algebra" comes from the Arabic word for "al-jabr" which means "restoration of balance" in both sides of an equation.. Algebra was based on previous work from Greeks, Alexandrians in Egypt, and Hindus who had preserved the work from ancient Egyptians and Babylonians. In the ninth century, al-Khwarizmi wrote one of the first Arabic algebras with both proofs and examples. Because of his work, he is called "the Father of Algebra." Al-Khwarizmi was a Persian born in the eighth century. He converted (changed) Babylonian and Hindu numerals into a workable system that almost anyone could use. He gave the name to his math as "al-jabr" which we know as "algebra". A Latin translation of al-Khwarizmi's book on algebra appeared in Europe in the 12th century. In the early 13th century the new algebra appeared in the writings of the famous Italian mathematician, Leonardo Fibonacci. So, algebra was brought into Europe from ancient Babylon, Egypt and India by the Arabs and then into Italy. C. Geometry The scholars at the House of Wisdom in Baghdad and at universities in Cairo, Egypt also contributed to geometry.

Geometry was highly developed by the Greeks, and the Muslims translated such great Greek thinkers as Euclid. Muslims used their understanding of geometry into designing wheels of all kinds, especially waterwheels and other systems for drawing up water, in improving farming equipment, and in designing devices of war such as catapults and crossbows. Geometry was also put to work in art, with beautiful geometric designs. Muslims further defined Euclidian geometry, and pointed the way toward the discovery of independent, non-Euclidean geometry developed in the most recent centuries. D. Trigonometry is also mostly a Muslim creation. It is a branch of mathematics which studies plane and spherical triangles. It developed from the need of astronomers to map points in the sky on a heavenly sphere. Trigonometry's functions, involving ratios such as sine and cosine, tangent and cotangent, were greatly developed and refined in the Islamic lands. E. Famous Muslim Mathematicians of the Middle Ages 1. Al-Khwarizmi (770 - 840 C.E.) was one of the greatest mathematicians who ever lived and is called the "Father of Algebra".

He also helped to bring "Arabic numerals" into use into the Islamic Empire, as well as later into Europe. He also demonstrated operations with fractions for the first time. Khwarizmi influenced the growth of science and mathematics. Several of his books were translated into many other languages, and were used as university textbooks until the 16th century. His approach was systematic and logical. He brought together the knowledge of his time on various branches of science, especially mathematics, and also added his original contributions. 2. Omar Khayyam (1044 - 1123 C.E.): Another great Muslim mathematician was Omar Khayyam. He is best known today for his poetry, but his contribution to mathematics was great. He showed how to express roots of cubic equations by line segments obtained by intersecting conic sections. Khayyam was an outstanding poet, mathematician, and astronomer. His work on algebra was known throughout Europe in the Middle Ages, and he also contributed to a calendar reform. Khayyam refers in his algebra book to Pascal's triangle. The algebra of Khayyam is geometrical, solving linear and quadratic equations by methods appearing in Euclid's Elements.

Khayyam also gave important results on ratios giving a new definition and extending Euclid's work to include the multiplication of ratios. He poses the question of whether a ratio can be regarded as a number but leaves the question unanswered. 3. Al-Khashi was born in 1390 in Kashan, Iran and died in 1450 in Samarkand (now Uzbek). He calculated � (pi) to 16 decimal places which was the best until about 1700. He considered himself the inventor of decimal fractions. He wrote The Reckoners' Key which summarizes arithmetic and contains work on algebra and geometry. 4. Al-Biruni (973 - 1048 C.E.) was a philosopher, astronomer, pharmacologist (one who studies drugs and herbs used for health), botanist (one who studies plants), geologist and mathematician. He translated Euclid's work into Sanskrit (an Indian language), and calculated the earth's circumference (distance around the earth) and radius (distance to the center) with an accuracy that is close to today's measurements. 5.

Nasir Al-Din Al-Tusi (1201 - 1274 C.E.) pioneered spherical trigonometry which includes six fundamental formulas for the solution of spherical right-angled triangles. One of his most important mathematical contributions was the treatment of trigonometry as a new mathematical discipline. He wrote on binomial coefficients which Pascal later introduced. (He can be called the "Father of Trigonometry".) He was also an astronomer philosopher, and medical scholar as well as a mathematician. Hindu-Arabic Numerals and how they came into Europe as "Arabic numerals" are explained. See other links at the bottom of this site. Also see how " Hindu" numerals came to Persia and Arabia, and then how "Arabic" numbers came into Europe . Read an overview of " Arab Contributions to Medieval mathematics ". It includes the contributions of Al-Khwarizmi, Abu Kamil Shuja (al'Hasib), Abu'l-Wafa, al-Karkhi, Omar Khayyam, and Al-Kashi.

Several biographies of scientists and mathematicians are found on on the Muslim Scholars Homepage : Al-Khwarizmi, Al-Kindi, Omar Khayyam, Al-Biruni, Nasir al-Din, and others. Learn about Mathematicians born in Iraq , including Al Khwarizmi. Biographies of Mathematicians by Dr. Zahoor are listed. Choose three or four of the most famous: al-Khwarizmi (algebra) [al-Khwarizmi is also here ], Omar Khyyam , al-Battani (trigonometry), al-Haitham (known as Alhazen in the West, developed analytical geometry by establishing linkage between algebra and geometry), al-Tusi (non-Euclidian geometry), and al-Biruni (who determined the circumference of the earth). See a chart comparing modern Arabic numerals with the earlier Arabic numerals developed in the Middle Ages (and influenced by the Hindu numerals with the concept of place value and the "zero"). Al-Khwarizmi (father of algebra); read another biography of Al-Khwarizmi . Read about Al-Khwarizmi and see one of his famous works on completing the square (shown below).

See Al-Khwarizmi for explanation. Arabic Mathematics is a somewhat difficult, but important article about the contributions of the Arabs in the field of mathematics. Also read another university level discussion about Arab Mathematics: Forgotten Brilliance? (St. Andrew's University, Scotland)

Question: Which scholar is known as the Father of Geometry?
Answer: EUCLID